Energy-limited escape revised

Abstract

Gas planets in close proximity to their host stars experience photoevaporative mass loss. The energy-limited escape concept is generally used to derive estimates for the planetary mass-loss rates. Our photoionization hydrodynamics simulations of the thermospheres of hot gas planets show that the energy-limited escape concept is valid only for planets with a gravitational potential lower than log 10 (−Φ G ) < 13.11 erg g −1 because in these planets the radiative energy input is efficiently used to drive the planetary wind. Massive and compact planets with log 10 (−Φ G ) 13.6 erg g −1 exhibit more tightly bound atmospheres in which the complete radiative energy input is re-emitted through hydrogen Lyα and free-free emission. These planets therefore host hydrodynamically stable thermospheres. Between these two extremes the strength of the planetary winds rapidly declines as a result of a decreasing heating efficiency. Small planets undergo enhanced evaporation because they host expanded atmospheres that expose a larger surface to the stellar irradiation. We present scaling laws for the heating efficiency and the expansion radius that depend on the gravitational potential and irradiation level of the planet. The resulting revised energy-limited escape concept can be used to derive estimates for the mass-loss rates of super-Earth-sized planets as well as massive hot Jupiters with hydrogen-dominated atmospheres.

Aeronomical constraints to the minimum mass and maximum radius of hot low-mass planets

“…This agrees well with calculations by Owen & Jackson (2012), who also estimated that η values higher than 40% are unrealistically high. More recently, Salz et al (2016) calculated the average heating efficiency for a set of planets with different masses and radii. They concluded that for planets with log(GM pl /R pl ) smaller than 13.11 (the case of the planets considered here), η is about 23%, independent of the planet parameters.…”

Young planets under extreme UV irradiation

“…The height-averaged heating efficiency (η) of the upper atmosphere exposed to high-energy stellar radiation is usually considered to be between 10% and 60% (e.g. Watson et al 1981;Yelle 2004;Murray-Clay et al 2009;Cecchi-Pestellini et al 2009;Owen & Jackson 2012;Shematovich et al 2014;Salz et al 2016). In this work, we follow the considerations of Erkaev et al (2016) and adopt a value of 15%, based on the results of the direct simulation Monte Carlo model calculations of Shematovich et al (2014), which model photolytic and electron impact processes in the thermosphere by solving the kinetic Boltzmann equation.…”

“…One dimensional models are widely used for exoplanet studies, particularly with respect to upper atmosphere modelling (see e.g. Murray-Clay et al 2009;Shaikhislamov et al 2014;Salz et al 2016;Erkaev et al 2016Erkaev et al , 2017Fossati et al 2017;Lammer et al 2016). An upgrade to 2D or 3D simulations is instead required to model the interaction between the expanding planetary atmosphere with the stellar wind, particularly when considering ion pick-up processes related to planetary atmospheric escape.…”

Strong H i Lyman-α variations from an 11 Gyr-old host star: a planetary origin?

“…In that case the age of the system puts upper limit on η at 40% and 130% for planets e and f, which means that even with conservative efficiencies of 10% , Salz et al 2016b) those planets would only have lost about 27% and 8% of their water content, respectively, after 11.2 Gy. Even though those results do not account for the temporal evolution of the stellar flux, and use simple assumption on the complex physics behind atmospheric escape, they leave open the possibility that the old planets of the Kepler-444 system could still be "hot Ganymedes" with a high water content.…”